He was pronounced dead at a local hospital on Friday, 10 days after taking the witness stand.
Mayor Eric Johnson said in a tweet Sunday that the department would "conduct a thorough investigation into the death of Joshua Brown", and urged people to not speculate about the case before the investigation is completed.
Authorities arrived at the Atera complex Saturday night to find a man lying on the ground in the parking lot with multiple gunshot wounds. Witnesses who heard the shots told officers they saw a four-door, silver sedan speeding away from the scene. No one else was shot.
"And then, I think she went back inside, then came back out", said Brown, who lived across the hallway from Jean.
Guyger testified that in September 2018, after working a long shift, she mistook Jean's apartment for her own and thought he was a burglar.
Then gunshots followed "right after", Mr Brown said.
Brown testified that he met Jean the day he was killed.
Former Dallas police officer Guyger was indicted on murder charges Friday, almost three months after she fatally shot an unarmed black neighbor whose apartment she said she entered by mistake, believing it to be her own. He was eating ice cream at the time. "Explaining what happened, what she thought happened".
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During Guyger's case, which lasted a full seven days, she admitted under cross-examination that she meant to kill Jean when she shot him.
The jury, made up largely of women and people of colour, could have sentenced her to up to life in prison or as little as two years.
Joshua Brown was only 28 years old.
She will be eligible for parole in five years.
The sentence angered Jean's family members and social justice advocates, who said it was another example of failing to hold white police officers like Guyger accountable for their actions.
Critics contend that it was unethical of Kemp to hug Guyger and give her the Bible.
"I don't know if this is possible but can I give her a hug please?"
Dozens of demonstrators marched through downtown Dallas to protest the sentence. She must, especially in a case that arouses passion and conflict like this one, stand for impartial justice. Kemp also said that Guyger asked her for a hug twice and after some hesitation, the judge embraced the former officer.
"I didn't want her to go back to the jail and to sink into doubt and self-pity and become bitter", Kemp said.
"I didn't do that from the bench", she said. An atheist group even filed a complaint against Kemp, alleging saying she violated the constitution by proselytizing and gifting her a bible. A Black bailiff in the courtroom patted the defendant's hair.
Brandt and Botham Jean's mother, Allison Jean, said she was surprised by her son's gesture of forgiveness.